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lfunc_lfunctions • Show schema
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{'Lhash': '3458873418843004746171076170036', 'a10': [1.8660254037844386, 3.232050807568877], 'a2': [-0.8660254037844386, 0.5], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.5, -0.8660254037844386], 'a5': [0.0, -3.732050807568877], 'a6': [0.8660254037844386, 0.5], 'a7': [2.366025403784439, 1.3660254037844386], 'a8': [0.0, 1.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [2.598076211353316, 2.5]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.49', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '1845282302671708266791972979529', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 3.732050807568877], [-5.0, 0]], 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'2-78-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.2479590486074333, 'root_number': '0.7116260690618662 + 0.7025584230735236*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.123979524304', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.72857001623338863597294091313', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.53422574343959597122805498660', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.70868088619909623586300094746', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '13.10', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/i/a/49/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-78-13.10-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-78-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.12397952430371666, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.72857001623338863597294091313', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3458873418843004746171076170036', 'Lhash_array': ['3458873418843004746171076170036'], 'label': '2-78-13.10-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/i/a/49/1'}